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Encinas Carrión, Santiago Bravo, Ana Guillán Rial, Javier 2025-07-02T08:58:16Z 2025-07-02T08:58:16Z 2025 Mathematische Nachrichten, 2025, p. 1-23 0025-584X https://uvadoc.uva.es/handle/10324/76184 10.1002/mana.12037 1 23 Mathematische Nachrichten 1522-2616 Producción Científica The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here, we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions. Este trabajo forma parte del proyecto de investigación: Ministerio de Ciencia e Innovación, Grant/Award Numbers: PID2022-138916NB-I00, CEX2019-000904-S, MCIN/AEI/10.13039/501100011033; Comunidad de Madrid; Agencia Estatal de Investigación, Grant/Award Number: CEX2020-001084-M; Ministerio de Ciencia e Innovacion, Grant/Award Number: PRE2021-100072 Open access funding provided by FEDER European Funds and the Junta De Castilla y León under the Research and Innovation Strategy for Smart Specialization (RIS3) of Castilla y León 2021-2027. application/pdf eng Wiley-VCH info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ © 2025 The Author(s) Attribution-NonCommercial-NoDerivatives 4.0 Internacional Asymptotic Samuel function Integral closure On some properties of the asymptotic Samuel function info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.12037 SI